Name
Title | ||
|---|---|---|
Absence of Gelation and Self-Similar Behavior for a Coagulation-Fragmentation Equation. |
Abstract | ||
|---|---|---|
The dynamics of a coagulation-fragmentation equation with multiplicative coagulation kernel and critical singular fragmentation is studied. In contrast to the coagulation equation, it is proved that fragmentation prevents the occurrence of the gelation phenomenon and a mass-conserving solution is constructed. The large time behavior of this solution is shown to be described by a self-similar solution. In addition, the second moment is finite for positive times whatever its initial value. The proof relies on the Laplace transform which maps the original equation to a first-order nonlinear hyperbolic equation with a singular source term. A precise study of this equation is then performed with the method of characteristics. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140976236 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
coagulation,singular fragmentation,mass conservation,self-similarity,Laplace transform,characteristics | Regular singular point,Mathematical optimization,Green's function for the three-variable Laplace equation,Mathematical analysis,Singular solution,Method of characteristics,Laplace's equation,Initial value problem,Partial differential equation,Mathematics,Hyperbolic partial differential equation | Journal |
Volume | Issue | ISSN |
47 | 3 | 0036-1410 |
Citations | PageRank | References |
1 | 0.97 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Philippe Laurençot | 1 | 30 | 10.30 |
| Henry van Roessel | 2 | 1 | 0.97 |